Ok, that was the next question of heat pump or no! So I need to state upfront that I am NOT the furnace/heat pump trained guy, so very limited!
But one point to check is that 12VDC battery is getting to the trermostat to be sent on as a signal to the furnace to start? That might lead to a simple fix if the fuse is blown?
Att he furnace a nd thermostat, there is a wire that should have a 2-3 letter code on the Winnebago wires. At the thermostast, you likely have to pull the wiring up out of the wall space to get to the Winnebago wiring that connects to the thermostat builders wires! They often change colors there so we can't find which wire without getting to the wires Winn adds to connect other builders items together.
The 12V comes to thermostat then when it calls for heat, that 12VDC is sent on wire JK toward the furnace as a first step to light.
But if that 12VDC is not getting to both furnace and thermostat, the fuse may be a problem to check.
This draawing of the fuse panel is shown looking from the back, so we need to trun it around to locate the fuse!
Shown as second from RIGHT on bottom row , so look for it on second from LEFT!!!
OR it might be labeled???
Not a furnace guy but that might get you started??